Abstract
We discuss some refinements of semiclassical calculations for the spin-wave excitation spectrum of easy-plane ferromagnets such as CsNi${\mathrm{F}}_{3}$ and examine their validity for low-spin values. We also introduce a new overcomplete set of spin states, which is used to derive integral representations and variational approximations for the partition function of magnetic chains with positive uniaxial anisotropy.
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